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Matematicheskie Zametki, 2019, Volume 105, Issue 2, Pages 240–250
DOI: https://doi.org/10.4213/mzm11939 (Mi mzm11939) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Aizerman Problem for Systems of Two Differential Equations

B. S. Kalitin

Belarusian State University
Full-text PDF (434 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm11939
Abstract: The stability of equilibria of systems of nonlinear ordinary differential equations is studied. A criterion for the reducibility of a second-order linear system to a scalar differential equation is given. Both positive definite and semidefinite Lyapunov functions are used to obtain sufficient conditions for the asymptotic stability (global stability) of second-order nonlinear differential equations. It is proved that the Aizerman problem has a positive solution with respect to the roots of the characteristic equation of two-dimensional systems of differential equations.
Keywords: system of differential equations, equilibrium, stability, Aizerman problem, Lyapunov functions.
Received: 24.01.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 2, Pages 227–235
DOI: https://doi.org/10.1134/S0001434619010255
Bibliographic databases:
Document Type: Article
UDC: 517.925
Language: Russian
Citation: B. S. Kalitin, “On the Aizerman Problem for Systems of Two Differential Equations”, Mat. Zametki, 105:2 (2019), 240–250; Math. Notes, 105:2 (2019), 227–235
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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